To find the volume of a sphere with a radius of [tex]\( 8 \text{ cm} \)[/tex] using [tex]\(\frac{22}{7}\)[/tex] for [tex]\(\pi\)[/tex], follow these steps:
1. Understand the formula for the volume of a sphere:
The formula to calculate the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where:
- [tex]\( V \)[/tex] is the volume
- [tex]\( \pi \)[/tex] is a constant (approximated here as [tex]\(\frac{22}{7}\)[/tex])
- [tex]\( r \)[/tex] is the radius of the sphere
2. Substitute the known values into the formula:
Given:
- Radius [tex]\( r = 8 \text{ cm} \)[/tex]
- [tex]\(\pi = \frac{22}{7}\)[/tex]
Substitute these values into the formula:
[tex]\[
V = \frac{4}{3} \times \frac{22}{7} \times (8)^3
\][/tex]
3. Calculate the cube of the radius:
First, find the cube of [tex]\( 8 \text{ cm} \)[/tex]:
[tex]\[
(8)^3 = 8 \times 8 \times 8 = 512
\][/tex]
4. Multiply with [tex]\(\pi\)[/tex] and simplify:
Next, plug in the cubed radius back into the volume formula:
[tex]\[
V = \frac{4}{3} \times \frac{22}{7} \times 512
\][/tex]
5. Simplify the expression step-by-step:
- First, compute [tex]\(\frac{4}{3} \times 512\)[/tex]:
[tex]\[
\frac{4}{3} \times 512 = \frac{4 \times 512}{3} = \frac{2048}{3}
\][/tex]
- Next, multiply by [tex]\(\frac{22}{7}\)[/tex]:
[tex]\[
V = \frac{2048}{3} \times \frac{22}{7} = \frac{2048 \times 22}{3 \times 7} = \frac{45056}{21}
\][/tex]
6. Convert the fraction to a decimal:
Finally, convert [tex]\(\frac{45056}{21}\)[/tex] to a decimal format to get the volume:
[tex]\[
\frac{45056}{21} \approx 2145.523809523809
\][/tex]
Therefore, the volume of the sphere with a radius of [tex]\( 8 \text{ cm} \)[/tex] using [tex]\(\frac{22}{7}\)[/tex] for [tex]\(\pi\)[/tex] is approximately [tex]\( 2145.52 \text{ cm}^3 \)[/tex].
